You won't be able start working until you get the EAD. Just don't mention
anything about this until they ask in the offer stage.
It is true that some companies don't like L2 applicants because its a
dependent visa, which means if your husband leaves his job, either
voluntarily or not, you would also have to leave your job. L1B visa holders
cannot change job, unless they transfer to a H1B or Greencard.
But otherwise, L2 is one of the best visas, you are not restricted to work
for any company, and normally you can extend to 5 years, which gives you
enough time to either into multiple H1B draws once a company takes you in.